index tweaks

[lambda.git] / assignment1.mdwn

diff --git a/assignment1.mdwn b/assignment1.mdwn
index 615e183..fa02cb8 100644 (file)
--- a/assignment1.mdwn
+++ b/assignment1.mdwn
@@ -40,9 +40,7 @@ evaluates to 10.
 
 <LI>Define an `and` operator.
 
 
 <LI>Define an `and` operator.
 

-<LI>Define an `xor` operator. 
-
-If you haven't seen this term before, here's a truth table:
+<LI>Define an `xor` operator. If you haven't seen this term before, here's a truth table:

 
     true xor true = false
     true xor false = true
 
     true xor true = false
     true xor false = true


@@ -93,13 +91,11 @@ Now we can write:
        (p get-first)   ; will evaluate to 10
        (p get-second)  ; will evaluate to 20
 
        (p get-first)   ; will evaluate to 10
        (p get-second)  ; will evaluate to 20
 

-If you're bothered by having the pair to the left and the function that
+If you're puzzled by having the pair to the left and the function that

 operates on it come second, think about why it's being done this way: the pair
 operates on it come second, think about why it's being done this way: the pair

-is a package that takes a function for operating on its elements as an
-argument, and returns the result of operating on its elemens with that
-function. In other words, the pair is also a function.  (Of course, in the
-untyped lambda calculus, absolutely *everything* is a function: functors,
-arguments, abstracts, redexes, values---everything.)
+is a package that takes a function for operating on its elements *as an
+argument*, and returns *the result of* operating on its elements with that
+function. In other words, the pair is a higher-order function. (Consider the similarities between this definition of a pair and a generalized quantifier.)

 
 If you like, you can disguise what's going on like this:
 
 
 If you like, you can disguise what's going on like this:
 


@@ -114,7 +110,7 @@ instead of:
 
        (p get-first)
 
 
        (p get-first)
 

-However, the latter is still what's going on under the hood.
+However, the latter is still what's going on under the hood. (Remark: `(lifted-f ((make-pair 10) 20))` stands to `(((make-pair 10) 20) f)` as `(((make-pair 10) 20) f)` stands to `((f 10) 20)`.)

 
 
 <OL start=13>
 
 
 <OL start=13>